What Are the Multiples of 9? Complete List, Examples for Kids

The multiples of 9 are numbers that can be divided by 9 with no remainder. The first multiples of 9 are 9, 18, 27, 36, 45, 54, 63, 72, 81, and 90. You can find them by multiplying 9 by 1, 2, 3, 4, and so on, or by adding 9 each time.

Understanding multiples of 9 is a key skill in the U.S. Common Core State Standards for Mathematics, covered in 4th grade under Operations & Algebraic Thinking (standard 4.OA.B.4). Students learn to determine whether a whole number is a multiple of a given one-digit number, recognize patterns, and use them to solve real-world problems.

What Are Multiples of 9?

A multiple of 9 is the product of 9 and a whole number.

For example:

• 9 × 1 = 9
• 9 × 2 = 18
• 9 × 3 = 27
• 9 × 4 = 36
• 9 × 5 = 45

So 9, 18, 27, 36, and 45 are multiples of 9.

Simple Rule

A multiple of 9 is any number that appears in the 9 times table.

If a number can be divided by 9 evenly, it is a multiple of 9.

Examples:

• 36 is a multiple of 9 because 36 ÷ 9 = 4 ✅
• 90 is a multiple of 9 because 90 ÷ 9 = 10 ✅
• 25 is not a multiple of 9 because 25 ÷ 9 leaves a remainder ❌

Formula for Multiples of 9

How to Explain Multiples of 9 Simply to a Child?

This is where multiples of 9 become really fun. They follow patterns that make them easy to spot.

1. Digit Sum Trick

If the digits add up to 9 or a multiple of 9, the number is a multiple of 9.

Examples:

• 45 → 4 + 5 = 9 ✅
• 72 → 7 + 2 = 9 ✅
• 162 → 1 + 6 + 2 = 9 ✅

If the sum is not 9, 18, 27, etc., then it’s not a multiple of 9.

This trick is part of the divisibility rule for 9, which you’ll see again later.

2. Finger Trick for 9 Times Table

Kids love this one!

1. Hold up both hands (10 fingers).
2. To find 9 × 4, bend down your 4th finger from the left.
3. Count fingers:

• Fingers on the left = tens
• Fingers on the right = ones

You’ll get 36!

This trick works for 9 × 1 through 9 × 10 and helps visual learners a lot.

3. Number Pattern in the Ones and Tens

Look at the multiples of 9:

• 09
• 18
• 27
• 36
• 45
• 54
• 63
• 72
• 81
• 90

Notice:

• The tens digit goes up by 1
• The ones digit goes down by 1

Advanced Concepts: Divisibility Rule for 9

The divisibility rule for 9 helps you check large numbers quickly.

The Core Rule

A number is divisible by 9 if and only if the sum of its digits is also divisible by 9.

How and Why It Works

In our number system, every place value (ones, tens, hundreds) is a power of 10. When you divide any power of 10 (like 10, 100, or 1000) by 9, the remainder is always 1.

This means a number like 567 is really:
(5 x 100) + (6 x 10) + (7 x 1)
When divided by 9, this is the same as:
(5 x 1) + (6 x 1) + (7 x 1) = 5 + 6 + 7
…which is just the sum of its digits (18).

Therefore, the original number (567) and the sum of its digits (18) will have the same remainder when divided by 9. If the digit sum is divisible by 9 (remainder 0), then the original number is also divisible by 9.

Examples

• Is 189 divisible by 9?
  Digit sum: 1 + 8 + 9 = 18.
  Since 18 ÷ 9 = 2 (no remainder), 189 is divisible by 9. (189 ÷ 9 = 21)
• Is 999 divisible by 9?
  Digit sum: 9 + 9 + 9 = 27.
  Since 27 ÷ 9 = 3, 999 is divisible by 9. (999 ÷ 9 = 111)
• Is 1,234 divisible by 9?
  Digit sum: 1 + 2 + 3 + 4 = 10.
  10 ÷ 9 = 1 with a remainder of 1. Therefore, 1,234 is NOT divisible by 9.

Related Concepts

• Divisibility Rule for 3: A number is divisible by 3 if the sum of its digits is divisible by 3. (This is related but a weaker condition than the rule for 9).
• Digit Sum: The foundation of this rule. You can repeat the digit sum process (e.g., for 99, 9+9=18, then 1+8=9) until you get a single digit.
• Casting Out Nines: A historical technique for checking arithmetic calculations, based on this same principle.
• Factors and Multiples: If a number ‘N’ is divisible by 9, then 9 is a factor of ‘N’, and ‘N’ is a multiple of 9.

Properties of Multiples of 9

Is 0 a Multiple of 9?

Yes, 0 is a multiple of 9. In fact, 0 is a multiple of every number. This is because 0 can be divided by any number without leaving a remainder. For example: 0 ÷ 9 = 0.

Are All Multiples of 9 Also Multiples of 3?

Yes. Every multiple of 9 is also a multiple of 3. This is because 9 itself is a multiple of 3.

Are the Multiples of 9 Always Odd or Even?

No. Multiples of 9 can be either odd or even:

• When 9 is multiplied by an odd number: 9 × 3 = 27 (odd)
• When 9 is multiplied by an even number: 9 × 2 = 18 (even)

How Many Multiples of 9 Are in 100?

To find how many multiples of 9 are in 100, divide 100 by 9 and keep only the whole number:

100 ÷ 9 = 11.11…

So there are 11 multiples of 9 in 100.

The multiples of 9 up to 100 are:

9, 18, 27, 36, 45,
54, 63, 72, 81, 90, 99

✅ Answer: 11 multiples of 9
❌ The next one, 108, is greater than 100.

First 20 Multiples of 9

Multiples of 9 Up to 100

The multiples of 9 up to 100 are:

9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99

Multiples of 9 Up to 150

The multiples of 9 up to 150 are:

9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126, 135, 144

What are the Multiples of 9 Up to 1000?

There are 111 positive multiples of 9 up to 1000.

• The first one is 9
• The last one below 1000 is 999

Common Multiples of 9 and Other Numbers

A common multiple is a number that is a multiple of both numbers at the same time.

The least common multiple (LCM) is the smallest common multiple of two numbers.Quick Summary Table

Quick Summary Table

Examples and Real-Life Applications

You might wonder: Where do we actually use multiples of 9?

Example 1: Money

If one toy costs $9:

• 3 toys cost 9 × 3 = 27 dollars
• 5 toys cost 9 × 5 = 45 dollars

Those totals are multiples of 9.

Example 2: Time and Calendars

• 9 minutes, 18 minutes, 27 minutes… all multiples of 9
• Many puzzles and math games use multiples of 9 to test number sense

Example 3: Classroom Math

Teachers often use multiples of 9 to:

• Teach patterns
• Introduce division
• Compare with other concepts like multiples of 3 or multiples of 6
  (You can explore those topics next for deeper understanding.)

Multiplication Tables

Multiplication Tables From 2-12

This collection of multiplication resources is designed to support mastery of Common Core State Standards for Operations and Algebraic Thinking. Specifically, it aligns with CCSS.MATH.CONTENT.3.OA.C.7, which requires students to fluently multiply and divide within 100, and 4.OA.B.4, focusing on factors and multiples. By exploring these tables, learners develop the algebraic foundation necessary for mental math fluency and higher-level problem solving.

FAQS

Final Thoughts

Remember, multiples of 9 are everywhere in math—and they follow some of the coolest patterns you’ll ever see.

Key Takeaways:

• Multiples of 9 come from 9 × whole numbers
• Their digits often add up to 9 or 18
• Easy tricks make them fun and simple to learn
• They help build strong number sense for future math topics

Try this next:Look around and see how many multiples of 9 you can spot today. Practice makes patterns stick!How many multiples of nine are there? When doing arithmetic, how can one avoid confusion? Remember to read this article from Wukong Math. The courses and teachers here will help you solve this problem.

James | WuKong Math Teacher

Graduated from Columbia University in the United States and has rich practical experience in mathematics competitions’ teaching, including Math Kangaroo, AMC… He teaches students the ways to flexible thinking and quick thinking in sloving math questions, and he is good at inspiring and guiding students to think about mathematical problems and find solutions.